A power system model parameter identifiability prior diagnosis method and device

Abstract

The application provides a power system model parameter identifiability prior diagnosis method and device, and relates to the technical field of power system model parameter checking. The method solves the problem that different parameters in the parameter checking process of the prior art are prone to similar response directions or even indistinguishable under selected characteristics, which leads to multiple solutions, compensation and iteration degradation, and the like. The method comprises the following steps: constructing a disturbance sample in a parameter prior range, and generating a multi-channel trajectory sensitivity sample library; performing mechanism information guided reconstruction characterization learning on trajectories in the multi-channel trajectory sensitivity sample library, and mapping information related to a target feature to a unified characterization space; based on obtained trajectory characterization results, forming a collinearity diagnosis result for parameter identification sufficiency; and identifying checkable parameters according to parameter separability and the collinearity diagnosis result. The method can directly identify checkable parameters, effectively identify risks, and avoid multiple solutions, non-convergence or local optimal solution problems in the checking result.

Description

Technical Field

[0001] This invention relates to the field of power system model parameter verification technology, and in particular to a method and apparatus for prior diagnosis of the identifiability of power system model parameters. Background Technology

[0002] In existing power system model parameter verification techniques, parameters with a significant impact on the system's dynamic response are typically selected as the objects to be corrected based on empirical judgment, sensitivity analysis, or posterior estimation results. Then, an objective function is constructed using the error between the measured trajectory and the simulated trajectory, and parameter identification is achieved through particle swarm optimization, Bayesian estimation, or other optimization methods. To improve the observability of the differences in the effects of different parameters, existing techniques often employ methods such as increasing measurement channels, introducing new error characteristic components, expanding the range of observation information, or improving search strategies to enhance the sensitivity of the objective function to parameter differences.

[0003] Furthermore, existing techniques often use the morphological characteristics of variable trajectories or their derived characteristics as the basis for parameter verification when constructing the objective function, assuming that the selected features can reflect the differences in the effects of different parameters on the system response. Based on this, parameter correction or optimal solution search is completed by comparing the trajectory fitting effects under different parameter combinations. This type of method can, to some extent, improve the discrepancy between simulation results and measured results, and therefore has become a common technical approach in the parameter verification of current power system dynamic models.

[0004] However, the existing technologies still have significant shortcomings: First, most existing methods evaluate the effect of parameter correction during or after parameter verification, lacking a pre-diagnostic mechanism to determine whether the given feature system is sufficient to support parameter identification before verification. Therefore, feature selection and parameter combination often rely on experience, lacking unified and verifiable quantitative criteria. Second, existing sensitivity analysis methods focus on the strength of the influence of a single parameter on the system response, without further determining whether the directions of action of different parameters overlap under the selected feature system. Therefore, even if some parameters have high sensitivity, they may still form substitutable relationships in the verification objective function due to similar response directions. Third, when different parameter perturbations produce approximately consistent responses under the selected features, the objective function's ability to distinguish between related parameter directions decreases, easily leading to problems such as non-unique parameter verification results, parameter compensation, iterative path back-and-forth adjustments, or insufficient convergence stability. Therefore, a method is urgently needed to quantitatively diagnose the separability, collinearity, and verification risks of parameters under a given feature system before parameter verification.

[0005] Therefore, existing power system model parameter verification methods generally lack a mechanism for pre-judging the identification support capability of a given feature system, feature selection mainly relies on experience and is difficult to quantitatively verify, and different parameters are prone to having similar or even indistinguishable response directions under the selected features, leading to multiple solutions, compensation and iterative degradation and other problems. Summary of the Invention

[0006] To address the problems in existing technologies where different parameters tend to have similar or even indistinguishable response directions under selected features during parameter verification, leading to multiple solutions, compensation, and iterative degradation, the present invention aims to provide a priori diagnostic method and apparatus for the identifiability of power system model parameters.

[0007] To address the aforementioned technical problems, in a first aspect, according to some embodiments, the present invention provides a priori diagnostic method for the identifiability of power system model parameters, characterized in that it includes:

[0008] The process involves constructing disturbance samples within the prior range of parameters and generating a multi-channel trajectory sensitivity sample library. Specifically, this includes: determining the set of candidate parameters to be diagnosed and their prior value ranges; performing multiple sets of disturbance sampling on each candidate parameter within the prior value range to obtain disturbance samples covering different parameter states; and for each set of disturbance samples, calculating the trajectory sensitivity of each candidate parameter to the target observation based on power system transient simulation to construct a multi-channel trajectory sensitivity sample library.

[0009] The trajectory in the multi-channel trajectory sensitivity sample library is subjected to mechanism-guided reconstruction representation learning to construct a mechanism-guided trajectory reconstruction representation mechanism, which maps information related to target features to a unified representation space;

[0010] Based on the obtained trajectory characterization results, the differences and overlap of response directions of different parameters under a given feature system are measured, the relationship between parameters is judged, and collinearity diagnosis results oriented towards parameter identification sufficiency are formed.

[0011] Based on the results of parameter separability and collinearity diagnosis, the risks of multiple solutions, compensation and iterative degradation under a given characteristic system are assessed, and verifiable parameters are identified.

[0012] Optionally, as one embodiment, the trajectory sensitivity is obtained using a center difference method, as follows:

[0013] For any parameter 'a' to be analyzed, its trajectory sensitivity can be obtained using the central difference method, as shown in Formula 1:

[0014] (1)

[0015] In the formula, Indicates time, Indicates parameters Sensitivity to system trajectory; Indicates parameters The amount of minute perturbation; and They represent the parameter values ​​respectively. and The corresponding state trajectory at that time; and These represent the corresponding algebraic variable trajectories.

[0016] Optionally, as one embodiment, the construction of the multi-channel trajectory sensitivity sample library specifically includes:

[0017] Obtained through Latin hypercube sampling Group of perturbation samples, the system has a total of The candidate parameters, and the multi-channel trajectory sensitivity sample library, are expressed by Formula 2, as follows:

[0018] (2)

[0019] In the formula, This represents a multi-channel trajectory sensitivity sample library; Indicates the total number of perturbed samples; This indicates the total number of candidate parameters to be diagnosed; This indicates the index of the perturbation sample. ; Indicates the index of the candidate parameter. ; Indicates the first The nth perturbation sample The multi-channel sensitivity trajectory corresponding to each candidate parameter, and ,in Indicates the number of observation channels. This indicates the length of the time-aligned sequence. The multi-channel trajectory sensitivity sample library is used to cover the parameter state regions that may be experienced during the parameter calibration process.

[0020] Optionally, as one embodiment, the mechanism-guided reconstruction representation learning specifically includes:

[0021] The encoding process is defined using Formula 3, as follows:

[0022] (3)

[0023] In the formula, Indicates the first Parameters for each sample The low-dimensional latent space representation; Represents the encoding mapping function; The input multi-channel sensitivity trajectory is represented; the encoder preferably uses a one-dimensional convolutional network, and the decoder preferably uses a multilayer perceptron to achieve low-dimensional encoding and trajectory reconstruction of the multi-channel sensitivity trajectory;

[0024] The trajectory reconstruction loss function is expressed as shown in Formula 4, as follows:

[0025] (4);

[0026] In the formula, Indicates the reconstruction loss; This represents the reconstructed trajectory output by the decoder; Represents the original input trajectory; Indicates smoothness Loss function;

[0027] Define the continuous feature supervision loss function as shown in Formula 5, as follows:

[0028] (5)

[0029] In the formula, This represents the monitoring loss for continuous mechanism characteristics; Indicates the total number of perturbed samples; Indicates the index of the perturbation sample; This indicates the total number of candidate parameters to be diagnosed; Indicates the index of the candidate parameter; The number of dimensions representing continuous mechanism features; Indicates continuous mechanism feature index, ; Indicates the first The nth perturbation sample The first candidate parameter corresponds to the sensitivity trajectory of the first... One true continuous mechanism characteristic value; This represents the corresponding continuous mechanism feature value predicted by the model; Indicates the first Weighting coefficients for continuous mechanism features; The loss function for continuous feature regression can be represented by mean squared error loss, mean absolute error loss, or smoothing loss. Loss. The continuous mechanism features include one or more of the following: trajectory decay exponent, dominant frequency, peak value, trough value, peak occurrence time, trough occurrence time, and recovery time.

[0030] To avoid misclassifying numerical noise, local disturbances, or weak oscillations as valid oscillations, this invention constructs an oscillation confidence-constrained gating loss. Let the oscillation prediction probability of the gating branch output be... Its corresponding tag is Meanwhile, based on the explicit oscillation intensity index of the sample... Constructing oscillation credibility Its definition is shown in Formula 6:

[0031] (6)

[0032] in, As the threshold for judging oscillation intensity, in one embodiment it can be 0.5, that is, the boundary between weak oscillation and strong oscillation is placed at the middle position of normalized intensity; Let be the confidence mapping coefficient. Therefore, the definition of the oscillation confidence constraint gated loss is as shown in Equation 7:

[0033] (7)

[0034] In the formula, This represents the oscillation confidence constraint gated loss; This represents a category-related weighting function used to mitigate the imbalance between positive and negative samples. This represents the binary cross-entropy loss; This is a penalty term for boundary ambiguity, when the predicted probability is close to... When the value is relatively large, it is used to suppress ambiguous decisions on high-confidence samples; This represents the oscillation confidence level obtained from the explicit oscillation intensity mapping; This is a credibility consistency term used to constrain the gated output to maintain consistency with the actual oscillation strength of the sample. and These are the weight coefficients for the boundary ambiguity penalty term and the credibility consistency term, respectively.

[0035] By combining trajectory reconstruction constraints, continuous feature supervision constraints, and optional oscillation confidence constraint gated loss, the total loss function is determined as shown in Formula 8, as follows:

[0036] (8)

[0037] In the formula, Indicates the total loss; This represents a continuous feature supervision weight function that gradually increases during the training process; Indicates the current number of training steps or training round; This indicates the maximum number of preheating steps or preheating cycles; This represents the maximum weight for continuous feature supervision; This represents a gated switch; when the oscillation-related semantics belong to the features of interest in the current task, it is selected. Otherwise take ;

[0038] In the early stages of training, priority is given to ensuring that the model learns a stable trajectory reconstruction capability. Subsequently, the role of mechanistic feature constraints in shaping the low-dimensional representation space is gradually strengthened. When necessary, oscillation confidence constraint gate loss is further used to suppress the interference of noise samples and boundary samples on the representation results, thereby obtaining a low-dimensional representation result that maintains the main dynamic shape of the original trajectory and reflects the established verification feature semantics.

[0039] Optionally, as one embodiment, measuring the differences and overlaps in the response directions of different parameters under a given characteristic system specifically includes:

[0040] The latent space vectors corresponding to all samples and all parameters are treated as the population sample set, and the population covariance matrix is ​​calculated. The Mahalanobis metric matrix As the inverse of the overall covariance matrix ;

[0041] Specifically, in the Under a perturbation sample, the parameter With parameters The consistency of the direction of action is given by the cosine similarity under the Mahalanobis metric, expressed by Formula Nine:

[0042] (9)

[0043] In the formula, Indicates the first Parameters under a perturbation sample With parameters Similarity; Indicates the index of the perturbation sample; and Indicates the index of the candidate parameter, and ; and They represent the first Parameters under a perturbation sample and parameters The low-dimensional latent space vector; This represents the population mean vector calculated from the latent space vectors of all perturbation samples and all candidate parameters; The Mahalanobis metric matrix can be obtained from the inverse of the population covariance matrix. This represents the transpose of a vector. The closer the value is to 1, the more consistent the direction of influence of the two parameters on the dynamic response of the system under the current characteristic system, and the stronger their substitutability.

[0044] Optionally, as one embodiment, the relationship between the determination parameters specifically includes:

[0045] The frequency and degree of collinearity within the statistical sample domain are used to classify collinearity patterns, including:

[0046] For parameter pairs In all The similarity results are calculated on each perturbed sample. Therefore, a sample-level similarity exceeding a threshold is defined. The frequency is shown in Formula 10:

[0047] (10)

[0048] In the formula, Indicates parameter pair The frequency that exceeds the limit; and Indicates the index of the candidate parameter, and ; Indicates the total number of perturbed samples; Indicates the index of the perturbation sample; Indicates the first Parameters under a perturbation sample With parameters Similarity; This indicates the threshold for determining if the similarity exceeds the limit; This indicates an indicator function, which takes the value 1 when the condition within the parentheses is true, and 0 otherwise. Formula 10 is used to characterize the frequency of high consistency events occurring across all perturbed samples.

[0049] To characterize the degree of discrimination when similarity falls below a threshold, a drop threshold is defined, as shown in Formula 11:

[0050] (11)

[0051] In the formula, Indicates parameter pair In the Relative threshold for each sample The amount of the drop; when hour, ;when hour, The larger the value, the easier it is for the two parameters to be distinguished in this sample;

[0052] Therefore, the volatility index is defined using Formula Twelve:

[0053] (12)

[0054] In the formula, Indicates parameter pair The degree of fluctuation; Indicates parameter pair The frequency exceeding the limit; and Indicates the index of the perturbation sample; and Representing parameter pairs respectively In the The and the first Similarity drop under each perturbation sample; Indicates parameter pair The average drop across all perturbation samples; Represents a very small positive number used to avoid a denominator of zero; prefix. This indicator is used to reduce the artificially high impact of a very small number of samples that do not exceed the limit or a very small number of samples that fall below the threshold on volatility. It reflects the degree to which the parameter's separability depends on changes in the parameter's state.

[0055] Based on over-limit frequency and volatility The collinearity mode of parameters is divided into three categories.

[0056] Set threshold and volatility threshold ,in It is used for both sample-level similarity exceeding the limit and exceeding the limit frequency. , In one embodiment, 0.9 is acceptable. 0.2 is acceptable.

[0057] when and When the parameter pair is determined to be a stable collinear parameter pair, it is considered to be a stable collinear parameter pair.

[0058] when When the parameter pair is determined to be a stable noncollinear parameter pair;

[0059] In other cases, the parameter pair is determined to be a conditionally collinear parameter pair.

[0060] Optionally, as one embodiment, the assessment of multiple solutions, compensation, and iterative degradation risks under a given feature system, and the identification of verifiable parameters, specifically includes:

[0061] To characterize whether a parameter pair exhibits a stable and significant indistinguishable relationship over the long term across all perturbed samples, a parameter pair is defined. The risk of global collinearity is shown in Formula Thirteen:

[0062] (13)

[0063] In the formula, Indicates parameter pair The risk of global collinearity; Indicates parameter pair The frequency that exceeds the limit; Indicates parameter pair The degree of fluctuation. When Larger and When the value is small, it indicates that the parameter pair maintains high similarity in a large number of perturbed samples and the collinearity is relatively stable, thus the risk of global collinearity is high.

[0064] To characterize whether collinear-noncollinear state switching occurs between parameter pairs in the local parameter space, define parameter pairs. In the The collinear event labels for each perturbation sample are defined using Formula Fourteen:

[0065] (14)

[0066] In the formula, Indicates parameter pair In the Does a collinear event occur under each perturbation sample? This indicates an indicator function that takes the value 1 if the condition within the parentheses is true, and 0 otherwise. Indicates the first Parameters under a perturbation sample With parameters Similarity; This indicates the threshold for determining if the similarity exceeds the limit. When... When, it indicates that the parameter is relative to the sample. Collinearity event occurs; when When, it indicates that the parameter is relative to the sample. No collinearity events occurred;

[0067] Let the first The parameter vector of each perturbation sample is Constructed based on Euclidean distance between samples Nearest neighbor graph, whose edge set is denoted as If the collinear event labels of samples at both ends of an edge are different, it is considered that the identifiability of that parameter pair has switched under a local small-range parameter change. The local flip rate is defined as shown in Formula 15:

[0068] (15)

[0069] In the formula, Indicates parameter pair Local flip rate; This indicates that the vector is constructed based on the perturbation sample parameter vector. Edge set of a nearest neighbor graph; Representing edge set The number of edges contained therein; Let an edge in the nearest neighbor graph be an edge that connects the first and second neighbors. The first perturbation sample and the second One perturbation sample; and Representing parameter pairs respectively In the The and the first Collinear event labels under a perturbation sample; This represents the XOR operation, where 1 is returned when the two labels are different, and 0 is returned when they are the same. The larger the value, the better the parameter is. The transition between collinear and non-collinear states is more likely to occur in the local parameter space.

[0070] Define a two-state coexistence gating factor, as shown in Formula 16:

[0071] (16)

[0072] In the formula, Indicates parameter pair Two-state coexisting gating factor; Indicates parameter pair The frequency of exceeding the limit; coefficient 4 is a normalization coefficient, making The range of values ​​is .when When the value is close to 0 or 1, it indicates that the parameter pairs are almost always non-collinear or almost always collinear. Approaching 0; when When the condition is such that collinear and non-collinear states coexist to the highest degree, then... The maximum value is 1.

[0073] Define parameter pairs The risk of partial handover is addressed using Formula 17:

[0074] (17)

[0075] In the formula, Indicates parameter pair Risk of partial switching; This represents a gating factor indicating the coexistence of two states; This represents the local flip rate. This metric considers whether parameter pairs simultaneously exist in collinear and non-collinear states within the sample domain, and whether they are prone to state switching in the local parameter space. It is mainly used to characterize the risk of oscillation, stagnation, or path degradation that conditionally collinear parameter pairs may cause in subsequent iterative verification.

[0076] The total risk score is defined using Formula 18:

[0077] (18)

[0078] In the formula, Indicates parameter pair Overall risk score; Indicates parameter pair The risk of global collinearity; Indicates parameter pair Risk of partial switching; This indicates taking the larger of the two values. When the parameter pair exhibits long-term stable collinearity, the total risk score is mainly dominated by global collinearity risk; when the parameter pair exhibits conditional collinearity, the total risk score is mainly dominated by local switching risk; when the parameter pair exhibits stable non-collinearity, both global collinearity risk and local switching risk are usually low, thus the total risk score is low.

[0079] Based on the total risk score, a screening result oriented towards parameter verification is generated. Let the set of parameters to be verified simultaneously be... Let the total risk threshold be... , For any candidate parameter If it is related to the set any other candidate parameter None of them constitute stable collinear parameter pairs, and the corresponding total risk scores Then determine the parameters Under a given feature system, it is suitable for direct verification; if the parameters With at least one candidate parameter They form stable collinear parameter pairs, or there exist For high-risk parameter pairs, then determine the parameter. It is not advisable to match the corresponding candidate parameters under the current feature system. Simultaneous verification requires fixing one of the parameters, merging parameter combinations, adding observation channels, supplementing mechanistic features, or adjusting the objective function before verification.

[0080] Secondly, embodiments of the present invention also provide a priori diagnostic device for the identifiability of power system model parameters, comprising:

[0081] The construction module is used to construct disturbance samples within the prior range of parameters and generate a multi-channel trajectory sensitivity sample library. Specifically, it includes: determining the set of candidate parameters to be diagnosed and their prior value range; performing multiple sets of disturbance sampling on each candidate parameter within the prior value range to obtain disturbance samples covering different parameter states; and for each set of disturbance samples, calculating the trajectory sensitivity of each candidate parameter to the target observation based on power system transient simulation to construct a multi-channel trajectory sensitivity sample library.

[0082] The learning module is used to perform mechanism-guided reconstruction representation learning on the trajectories in the multi-channel trajectory sensitivity sample library, construct a mechanism-guided trajectory reconstruction representation mechanism, and map information related to target features to a unified representation space.

[0083] The diagnostic module is used to measure the differences and overlaps in the response directions of different parameters under a given feature system based on the obtained trajectory representation results, determine the relationship between parameters, and form collinearity diagnostic results oriented towards the sufficiency of parameter identification.

[0084] The judgment module is used to assess the risk of multiple solutions, compensation, and iterative degradation under a given characteristic system based on the results of parameter separability and collinearity diagnosis, and to identify verifiable parameters.

[0085] Thirdly, according to embodiments of the present invention, an electronic device is also provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described in any of the first aspects above.

[0086] Fourthly, according to embodiments of the present invention, a computer-readable storage medium is also provided, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the steps of the method described in any of the first aspects above.

[0087] The above-mentioned technical solution of the present invention has at least the following beneficial technical effects: This solution performs multiple sets of disturbance sampling on each candidate parameter within the prior value range to obtain disturbance samples covering different parameter states; for each set of disturbance samples, based on power system transient simulation, the trajectory sensitivity of each candidate parameter to the target observation is calculated, and a multi-channel trajectory sensitivity sample library is constructed. This application generates disturbance samples within the allowable parameter range and calculates the multi-channel sensitivity trajectory of each parameter on the selected observation, enabling the diagnostic results to cover the state regions that may be experienced during the parameter verification process; this application extracts mechanistic information from the trajectories in the multi-channel trajectory sensitivity sample library. This application employs a mechanism-guided trajectory reconstruction representation learning approach. By mapping sensitivity trajectories to a low-dimensional representation space consistent with task-specific semantics, and simultaneously applying trajectory reconstruction constraints and mechanism feature supervision, the latent space retains both the original trajectory morphology information and dynamic features closely related to parameter identification, such as damping, dominant frequency, and peak-valley timing. This application uses similarity assessment of parameter action directions based on latent space vectors, rather than directly comparing point-to-point differences in the original trajectories. Instead, it utilizes the directional consistency between latent space vectors to characterize whether the influence patterns of different parameters on the system's dynamic response tend to overlap, serving as the basis for parameter collinearity diagnosis. Therefore, this application directly identifies which parameters can be verified and which cannot, constructing a priori framework system to effectively identify risks, avoid multiple solutions in verification results, and prevent iterative, non-convergent, or locally optimal problems during the verification process. Attached Figure Description

[0088] To more clearly illustrate the technical solutions in the embodiments of the present invention or in the conventional art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0089] Figure 1 This is a schematic diagram of a priori diagnostic method for the identifiability of power system model parameters provided in an embodiment of the present invention.

[0090] Figure 2 This is a schematic diagram of a trajectory reconstruction architecture provided in an embodiment of the present invention.

[0091] Figure 3 This is a diagram of a WSCC3 9-node system provided in an embodiment of the present invention.

[0092] Figure 4 This is a demonstration of the trajectory reconstruction training effect provided by an embodiment of the present invention.

[0093] Figure 5It is the Gen1- provided in the embodiments of the present invention. &Gen1- A schematic diagram of the trajectory correction results.

[0094] Figure 6 The parameters provided in this embodiment of the invention are the correction results for the A&B trajectories.

[0095] Figure 7 This refers to the tortuosity of the parameter update path for parameters A and B provided in the embodiments of the present invention.

[0096] Figure 8 This is a schematic block diagram of a priori diagnostic device for the identifiability of power system model parameters provided in an embodiment of the present invention.

[0097] Figure 9 This is a schematic block diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0098] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0099] Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the present invention.

[0100] It should be noted that the sequence number mentioned in this application does not necessarily mean that the execution must be strictly in the correct order in the actual implementation process. The sequence number is used to distinguish each step, facilitate explanation, and prevent confusion.

[0101] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0102] To address the common problems in existing power system model parameter verification methods, such as the lack of a mechanism for pre-judging the identification support capability of a given feature system, the reliance on experience for feature selection which is difficult to quantitatively verify, and the tendency for different parameters to exhibit similar or even indistinguishable response directions under selected features, leading to multiple solutions, compensation, and iterative degradation, this paper proposes a priori diagnostic method for parameter identifiability based on sensitivity trajectory reconstruction. Before the parameter verification is implemented, this method quantitatively assesses the separability, collinearity, and potential verification risks of parameter actions under the target feature system. This provides a basis for target parameter selection, feature supplementation, and verification strategy adjustment, thereby improving the stability, reliability, and credibility of parameter verification results from the source.

[0103] The construction approach of this application is as follows:

[0104] (1) Construct a trajectory sensitivity sample base that can characterize the differences in the effects of target parameters.

[0105] Based on the power system model to be analyzed, candidate parameters are perturbed within the prior parameter range. Response information of parameter changes to multi-channel observation trajectories is obtained through system dynamic simulation, forming a trajectory sensitivity sample library covering different parameter states. This serves as the data foundation for subsequent identifiable diagnostics. The purpose of this step is not to directly verify parameters, but to provide unified sample support for determining whether the effects of different parameters are distinguishable under a given characteristic system.

[0106] (2) Establish a trajectory reconstruction representation that is consistent with the characteristics of the verification task.

[0107] To address the issues of high computational cost and difficulty in reflecting task-related mechanistic information such as damping, dominant frequency, and peak-valley timing when directly comparing large-scale, multi-channel sensitivity trajectories, a trajectory reconstruction representation mechanism guided by mechanistic information is constructed. While maintaining the main dynamic form of the original trajectory, information related to target features is mapped to a unified representation space, thus providing a basis for stable comparison of different parameter directions.

[0108] (3) Achieve quantitative diagnosis of the separability of the action directions of different parameters.

[0109] Based on the obtained trajectory representation results, the differences and overlaps in the response directions of different parameters under a given feature system are measured. This allows for the determination of whether different relationships exist between the parameters, such as long-term high similarity, local dependency changes, or overall separability. Based on this, a collinearity diagnostic result oriented towards the sufficiency of parameter identification is formed. The core of this step lies in transforming the question of "whether the features are sufficient to support parameter identification" into a calculable and comparable quantitative problem.

[0110] (4) Output risk prediction results for subsequent parameter verification.

[0111] Based on the results of parameter separability and collinearity diagnosis, the potential risks of multiple solutions, compensation and iterative degradation under the given feature system are further evaluated, forming a priori judgment basis for adjusting the target parameter combination, feature supplementation and verification strategy. This allows for the identification of unfavorable factors before parameter verification is implemented, reducing the probability of ill-posedness and convergence degradation in the subsequent verification process.

[0112] The following is an explanation.

[0113] refer to Figure 1 As shown, a priori diagnostic method for the identifiability of power system model parameters includes:

[0114] S1. Constructing disturbance samples within the prior range of parameters and generating a multi-channel trajectory sensitivity sample library, specifically including: determining the set of candidate parameters to be diagnosed and their prior value range; performing multiple sets of disturbance sampling on each candidate parameter within the prior value range to obtain disturbance samples covering different parameter states; for each set of disturbance samples, calculating the trajectory sensitivity of each candidate parameter to the target observation quantity based on power system transient simulation, and constructing a multi-channel trajectory sensitivity sample library;

[0115] S2. Perform mechanism-guided reconstruction representation learning on the trajectories in the multi-channel trajectory sensitivity sample library, construct a mechanism-guided trajectory reconstruction representation mechanism, and map information related to target features to a unified representation space;

[0116] S3. Based on the obtained trajectory representation results, measure the difference and overlap of the response directions of different parameters under the given feature system, judge the relationship between the parameters, and form a collinearity diagnosis result oriented towards the sufficiency of parameter identification.

[0117] S4. Based on the results of parameter separability and collinearity diagnosis, assess the risks of multiple solutions, compensation and iterative degradation under a given characteristic system, and identify verifiable parameters.

[0118] The following is a detailed explanation.

[0119] 1. Establish a dynamic model of the power system after disturbance and calculate the trajectory sensitivity of the target parameters.

[0120] The dynamic behavior of a power system after a disturbance can be represented by a system of differential-algebraic equations:

[0121]

[0122] In the formula, Indicates time; Represents system state variables; Represents system algebraic variables; Represents the system parameter vector; and These represent the differential equation and algebraic equation of the system, respectively. This equation illustrates that the dynamic response of the system is simultaneously influenced by state variables, algebraic variables, and parameter variables.

[0123] For any parameter to be analyzed Its trajectory sensitivity can be obtained using the central difference method:

[0124] (1)

[0125] In the formula, Indicates parameters Sensitivity to system trajectory; Indicates parameters The amount of minute perturbation; and They represent the parameter values ​​respectively. and The corresponding state trajectory at that time; and These represent the trajectories of the corresponding algebraic variables. This step is used to determine how different parameters affect the dynamic response.

[0126] 2. Construct perturbation samples within the prior parameter range and form a multi-channel sensitivity sample library.

[0127] Considering that the sensitivity trajectory in a high-order nonlinear power system changes with parameter states, and that the parameter verification process itself is an iterative update process, a one-time analysis cannot be performed only at the initial operating point. Instead, a disturbance sample set should be constructed within the allowable parameter range. Let's assume that the disturbance sample set is obtained through Latin hypercube sampling. Group of perturbation samples, the system has a total of With candidate parameters, the multi-channel sensitivity sample library can be expressed as:

[0128] (2)

[0129] In the formula, Represents the sensitivity sample library; Indicates the first One perturbation sample; Indicates the first One candidate parameter; Indicates the first Parameters for each sample The multi-channel sensitivity trajectory; preferably, ,in To observe the number of channels, This is the length of the time-aligned sequence. This sample library is used to cover the parameter state regions that may occur during the parameter verification process.

[0130] 3. Reconstruction representation learning guided by mechanistic information for multi-channel sensitivity trajectories.

[0131] To avoid the excessive computational cost of directly comparing trajectories on a large-scale sample database, and to address the difficulty in representing the mechanistic information of interest to the objective function, such as damping, dominant frequency, and peak-valley timing, through simple point-to-point trajectory distance, this invention introduces a trajectory reconstruction representation mechanism guided by mechanistic information. Its encoding process is expressed as follows:

[0132] ;

[0133] In the formula, Indicates the first Parameters for each sample The low-dimensional latent space representation; Represents the encoding mapping function; This represents the input multi-channel sensitivity trajectory. The encoder preferably employs a one-dimensional convolutional network, and the decoder preferably employs a multilayer perceptron to achieve trajectory reconstruction.

[0134] To ensure that the latent space representation retains the main shape of the original trajectory, a trajectory reconstruction loss is employed:

[0135] (3)

[0136] In the formula, Indicates the reconstruction loss; This represents the reconstructed trajectory output by the decoder; Represents the original input trajectory; Indicates smoothness Loss function. This loss exhibits quadratic penalty in the small error interval and linear penalty in the large error interval, which is beneficial for suppressing local anomalies and noise interference.

[0137] For continuous mechanistic features of interest to the target task, such as damping, dominant frequency, peak value, valley value, peak and valley occurrence time, and recovery time, a continuous feature supervision loss can be defined:

[0138] (4)

[0139] In the formula, This represents the monitoring loss for continuous mechanism characteristics; Indicates the total number of perturbed samples; Indicates the index of the perturbation sample; This indicates the total number of candidate parameters to be diagnosed; Indicates the index of the candidate parameter; The number of dimensions representing continuous mechanism features; Indicates continuous mechanism feature index, ; Indicates the first The nth perturbation sample The first candidate parameter corresponds to the sensitivity trajectory of the first... One true continuous mechanism characteristic value; This represents the corresponding continuous mechanism feature value predicted by the model; Indicates the first Weighting coefficients for continuous mechanism features; The loss function for continuous feature regression can be represented by mean squared error loss, mean absolute error loss, or smoothing loss. Loss. The continuous mechanism features include one or more of the following: trajectory decay exponent, dominant frequency, peak value, trough value, peak occurrence time, trough occurrence time, and recovery time.

[0140] To avoid misclassifying numerical noise, local disturbances, or weak oscillations as valid oscillations, this invention constructs an oscillation confidence-constrained gating loss. Let the oscillation prediction probability of the gating branch output be... Its corresponding tag is Meanwhile, based on the explicit oscillation intensity index of the sample... Constructing oscillation credibility Its definition is:

[0141] (5)

[0142] in, As the threshold for judging oscillation intensity, in one embodiment it can be 0.5, that is, the boundary between weak oscillation and strong oscillation is placed at the middle position of normalized intensity; Let be the confidence mapping coefficient. Therefore, the oscillation confidence constraint gating loss is defined as:

[0143] (6)

[0144] In the formula, This represents the oscillation confidence constraint gated loss; This represents a category-related weighting function used to mitigate the imbalance between positive and negative samples. This represents the binary cross-entropy loss; This is a penalty term for boundary ambiguity, when the predicted probability is close to... When the value is relatively large, it is used to suppress ambiguous decisions on high-confidence samples; This represents the oscillation confidence level obtained from the explicit oscillation intensity mapping; This is a credibility consistency term used to constrain the gated output to maintain consistency with the actual oscillation strength of the sample. and These are the weight coefficients for the boundary ambiguity penalty term and the credibility consistency term, respectively.

[0145] By combining trajectory reconstruction constraints, continuous feature supervision constraints, and optional oscillation confidence constraint gated loss, the total loss function is determined as shown in Equation 7, as follows:

[0146] (7)

[0147] In the formula, Indicates the total loss; This represents a continuous feature supervision weight function that gradually increases during the training process; Indicates the current number of training steps or training round; This indicates the maximum number of preheating steps or preheating cycles; This represents the maximum weight for continuous feature supervision; This represents a gated switch; when the oscillation-related semantics belong to the features of interest in the current task, it is selected. Otherwise take ;

[0148] In the early stages of training, priority is given to ensuring that the model learns a stable trajectory reconstruction capability. Subsequently, the role of mechanistic feature constraints in shaping the low-dimensional representation space is gradually strengthened. When necessary, oscillation confidence constraint gate loss is further used to suppress the interference of noise samples and boundary samples on the representation results, thereby obtaining a low-dimensional representation result that maintains the main dynamic shape of the original trajectory and reflects the established verification feature semantics.

[0149] The overall trajectory reconstruction framework is as follows Figure 2 As shown.

[0150] 4. Calculate the similarity of the action directions of parameters based on latent space representation.

[0151] After obtaining the latent space vectors corresponding to all samples and all parameters, we treat them as the overall sample set and calculate the overall covariance matrix. And define the Mahalanobis metric matrix. That is, the inverse of the total covariance matrix. This step is used to eliminate the impact of scale differences across different latent space dimensions on similarity assessment.

[0152] Furthermore, in the Under a perturbation sample, the parameter With parameters The consistency of the direction of action is given by the cosine similarity under the Mahalanobis metric:

[0153] (8)

[0154] In the formula, Indicates the first Parameters under a perturbation sample With parameters Similarity; Indicates the index of the perturbation sample; and Indicates the index of the candidate parameter, and ; and They represent the first Parameters under a perturbation sample and parameters The low-dimensional latent space vector; This represents the population mean vector calculated from the latent space vectors of all perturbation samples and all candidate parameters; The Mahalanobis metric matrix can be obtained from the inverse of the population covariance matrix. This represents the transpose of a vector. The closer the value is to 1, the more consistent the direction of influence of the two parameters on the dynamic response of the system under the current characteristic system, and the stronger their substitutability.

[0155] 5. Statistically analyze the frequency and degree of collinearity within the sample domain, and classify the collinearity patterns.

[0156] For parameter pairs In all The similarity results are calculated on each perturbed sample. Therefore, a sample-level similarity exceeding a threshold is defined. The frequency is:

[0157] (9)

[0158] In the formula, Indicates parameter pair The frequency that exceeds the limit; and Indicates the index of the candidate parameter, and ; Indicates the total number of perturbed samples; Indicates the index of the perturbation sample; Indicates the first Parameters under a perturbation sample With parameters Similarity; This indicates the threshold for determining if the similarity exceeds the limit; This indicates an indicator function that takes the value 1 when the condition within the parentheses is true, and 0 otherwise. This metric is used to characterize how frequently a parameter pair exhibits high consistency events across all perturbed samples.

[0159] To characterize the degree of discrimination when similarity falls below a threshold, the drop threshold is defined as follows:

[0160] (10)

[0161] In the formula, Indicates parameter pair In the Relative threshold for each sample The amount of the drop; when hour, ;when hour, The larger the value, the easier it is for the two parameters to be distinguished in this sample;

[0162] Therefore, the volatility indicator is defined as follows:

[0163] (11)

[0164] In the formula, Indicates parameter pair The degree of fluctuation; Indicates parameter pair The frequency that exceeds the limit; and Indicates the index of the perturbation sample; and Representing parameter pairs respectively In the The and the first Similarity drop under each perturbation sample; Indicates parameter pair The average drop across all perturbation samples; Represents a very small positive number used to avoid a denominator of zero; prefix. This indicator is used to reduce the artificially high impact of a very small number of samples that do not exceed the limit or a very small number of samples that fall below the threshold on volatility. It reflects the degree to which the parameter's separability depends on changes in the parameter's state.

[0165] Based on over-limit frequency and volatility The collinearity mode of parameters is divided into three categories.

[0166] Set threshold and volatility threshold ,in It is used for both sample-level similarity exceeding the limit and exceeding the limit frequency. , In one embodiment, 0.9 is acceptable. 0.2 is acceptable.

[0167] when and When the parameter pair is determined to be a stable collinear parameter pair, it is considered to be a stable collinear parameter pair.

[0168] when When the parameter pair is determined to be a stable noncollinear parameter pair;

[0169] In other cases, the parameter pair is determined to be a conditionally collinear parameter pair.

[0170] Among them, stable collinear parameter pairs indicate that the parameter pairs consistently exhibit high consistency across a wide range of samples; stable noncollinear parameter pairs indicate that they are essentially separable across a wide range of samples; and conditionally collinear parameter pairs indicate that their separability switches as the parameter states change.

[0171] 6. Correction risk score for the three types of parameter pairs.

[0172] To ensure that risk assessment applies not only to conditionally collinear parameter pairs but also covers stable collinear and stable non-collinear parameter pairs, this invention, after classifying parameter pairs for collinearity, further constructs a unified risk score for all parameter pairs. This unified risk score comprises three parts: global collinearity risk, local switching risk, and a total risk score.

[0173] First, to characterize whether a stable and significant indistinguishable relationship exists between parameter pairs across the entire perturbed sample range, parameter pairs are defined. The risk of global collinearity is:

[0174] (12)

[0175] In the formula, Indicates parameter pair The risk of global collinearity; Indicates parameter pair The frequency that exceeds the limit; Indicates parameter pair The degree of fluctuation. When Larger and When the value is small, it indicates that the parameter pair maintains high similarity in a large number of perturbed samples and the collinearity is relatively stable, thus the risk of global collinearity is high.

[0176] Furthermore, to characterize whether parameter pairs are prone to "collinear-noncollinear" state switching in the local parameter space, parameter pairs are first defined. In the The collinear event labels for each perturbation sample are:

[0177] (13)

[0178] In the formula, Indicates parameter pair In the Does a collinear event occur under each perturbation sample? This indicates an indicator function that takes the value 1 if the condition within the parentheses is true, and 0 otherwise. Indicates the first Parameters under a perturbation sample With parameters Similarity; This indicates the threshold for determining if the similarity exceeds the limit. When... When, it indicates that the parameter is relative to the sample. Collinearity event occurs; when When, it indicates that the parameter is relative to the sample. No collinearity event occurred.

[0179] Let the first The parameter vector of each perturbation sample is Constructed based on Euclidean distance between samples Nearest neighbor graph, whose edge set is denoted as If the collinear event labels of samples at both ends of an edge are different, it is considered that the identifiability of that parameter pair has switched under a local, small-scale parameter change. The local flip rate is thus defined as:

[0180] (14)

[0181] In the formula, Indicates parameter pair Local flip rate; This represents the number of edges in the nearest neighbor graph; Let an edge in the nearest neighbor graph be an edge that connects the first and second neighbors. The first perturbation sample and the second One perturbation sample; and Representing parameter pairs respectively In the The and the first Collinear event labels under a perturbation sample; This represents the XOR operation. The larger the value, the easier it is for the parameter pair to undergo identifiable switching in the local parameter space.

[0182] Considering that local flipping only truly poses a risk to subsequent verification when parameter pairs simultaneously possess multiple collinear and non-collinear states within the sample domain, the two-state coexistence gating factor is defined as:

[0183] (15)

[0184] In the formula, Indicates parameter pair Two-state coexisting gating factor; Indicates parameter pair The frequency of exceeding the limit; coefficient 4 is a normalization coefficient, making The range of values ​​is .when When the value is close to 0 or 1, it indicates that the parameter pairs are almost always non-collinear or almost always collinear. Approaching 0; when When the condition is such that collinear and non-collinear states coexist to the highest degree, then... The maximum value is 1.

[0185] Therefore, parameter pairs are defined. The risks of partial handover are:

[0186] (16);

[0187] In the formula, Indicates parameter pair Risk of partial switching; This represents a gating factor indicating the coexistence of two states; This represents the local flip rate. This metric considers whether parameter pairs simultaneously exist in collinear and non-collinear states within the sample domain, and whether they are prone to state switching in the local parameter space. It is mainly used to characterize the risk of oscillation, stagnation, or path degradation that conditionally collinear parameter pairs may cause in subsequent iterative verification.

[0188] Finally, to provide a unified risk output for the three parameter pairs, the total risk score is defined as:

[0189] (17);

[0190] In the formula, Indicates parameter pair Overall risk score; Indicates parameter pair The risk of global collinearity; Indicates parameter pair Risk of partial switching; This indicates taking the larger of the two values. When the parameter pair exhibits long-term stable collinearity, the total risk score is mainly dominated by global collinearity risk; when the parameter pair exhibits conditional collinearity, the total risk score is mainly dominated by local switching risk; when the parameter pair exhibits stable non-collinearity, both global collinearity risk and local switching risk are usually low, thus the total risk score is low.

[0191] Based on the total risk score, a screening result oriented towards parameter verification is generated. Let the set of parameters to be verified simultaneously be... Let the total risk threshold be... , For any candidate parameter If it is related to the set any other candidate parameter None of them constitute stable collinear parameter pairs, and the corresponding total risk scores Then determine the parameters Under a given feature system, it is suitable for direct verification; if the parameters With at least one candidate parameter They form stable collinear parameter pairs, or there exist For high-risk parameter pairs, then determine the parameter. It is not advisable to match the corresponding candidate parameters under the current feature system. Simultaneous verification requires fixing one of the parameters, merging parameter combinations, adding observation channels, supplementing mechanistic features, or adjusting the objective function before verification.

[0192] To further illustrate the effects of the present invention, corresponding numerical examples are provided below for verification.

[0193] 1. Verification through numerical examples.

[0194] Based on the simulation tool PSASP, a simulation analysis is performed using the WSCC3-machine 9-node system as an example (e.g.) Figure 3 (As shown). Node 8 is configured with a three-phase short-circuit fault, lasting 0.1 s. The generator model is a fourth-order model, and the load model is a constant power model. The target parameters include those of the three generators (Gen) and their excitation system voltage regulators (AVRs), totaling 36 parameters. These include the d-axis and q-axis reactances of the generators. , transient reactance , and transient open-circuit time constant , The inertial time constant of the generator Gain coefficient of excitation system voltage regulator and time constant Negative feedback gain coefficient and time constant Excitation cycle time constant The case study analyzes the voltage and active power trajectories at the fault node, focusing on those aspects that operators typically focus on and that are important for system safety.

[0195] The trajectory simulated by the component parameters in the standard example is regarded as the simulation trajectory before parameter correction; by randomly perturbing the target parameters, simulation is performed based on the parameter data after perturbation, and the simulation result is regarded as the real PMU measurement trajectory of the system after adding Gaussian noise.

[0196] The target parameters are randomly perturbed using the LHS method, with the perturbation rate defined as ±30% of their original value to avoid parameter values ​​that do not conform to physical reality. The example uses a physically constrained autoencoder to learn the trajectory sensitivity, with the input being a filtered dual-channel sensitivity trajectory sequence of samples. The encoder employs three layers of one-dimensional convolution (32 / 64 / 128), and the decoder uses two layers of MLP (256→128) followed by a linear output layer. Additionally, a physical supervision branch (64→64) is added in the latent space for physical consistency constraints.

[0197] Figure 4 This demonstrates the reconstruction error and waveform correlation of the model on the sample set before and after initialization (before training). Regarding waveform consistency ( Figure 4 (a) The median correlation coefficient between the trained trajectory and the original data reached 0.9611, with a mean of 0.9206, and the RMSE ( Figure 4 (b) The median decreased from 0.1253 to 0.0306. This indicates that the model can well preserve the overall shape and phase change trend of the trajectory on the target samples, and can still maintain acceptable consistency on low-quality samples.

[0198] This example defines the over-limit frequency threshold. Volatility threshold Based on the trained model, the reconstructed trajectories of all samples can be explicitly output. The reconstructed trajectories corresponding to each parameter in the samples are calculated in pairs according to the cosine similarity under Mahalanobis metric, and then the output results are statistically analyzed. The calculation results show that among 630 parameter pairs, one pair of stable collinear parameter pairs was identified, namely parameter pair Gen1- & Gen1- The collinear over-limit frequency of this parameter pair It is 94.35%, volatility The percentage is 2.61%; there are 619 pairs of stable non-collinear parameter pairs; and 10 pairs of conditionally collinear parameter pairs. Table 1 shows the over-limit frequencies of these parameter pairs. volatility And the local flip rate defined for the collinearity parameters that may occur during the iterative correction process under such conditions. and comprehensive risk score .

[0199] Table 1. Conditional collinearity parameter pairs are shown in the table below.

[0200]

[0201] In given characteristics To verify the effectiveness of the relevant risk assessment method under the damping characteristics of the trajectory, two numerical examples are constructed based on the collinearity calculation results of the parameters to validate the effectiveness of the research method. The objective function is defined. , by trajectory shape and Together they constitute:

[0202] .

[0203] Under the established feature system, to verify the predictive ability of the risk assessment method for the subsequent parameter verification process, two types of verification examples are constructed based on the above collinearity diagnosis results. The first type of example selects parameter pairs diagnosed as stable collinear to verify whether such parameter pairs still exhibit multiple solutions or parameter compensation phenomena when the trajectory fitting effect is good. The second type of example selects conditionally collinear parameter pairs with different risk scores to verify whether the local switching risk can reflect the differences in path degradation and convergence stability during the parameter verification iteration process.

[0204] 2. Risk verification based on collinearity parameter correction.

[0205] Parameters for Gen1- & Gen1- These are identified collinear parameter pairs. Therefore, this example performs random perturbations on these two parameters in a 3-machine 9-node system. The simulated trajectory based on the perturbated parameters is used as the measured trajectory, and the two parameters are corrected based on the initial data. The calibration method uses the particle swarm optimization algorithm, with a fixed number of particles of 15, and the convergence threshold is defined as... The simulation does not restrict the seed to random, allowing for a random initial particle distribution. Multiple parameter adjustments to the two parameters are then performed to obtain multiple parameter pairs for Gen1-. & Gen1- Correction results.

[0206] Figure 5 The results are shown after 50 corrections to this parameter pair. Figure 5 (a) Shows the parameters Gen1- after 50 parameter corrections. and Gen1- The numerical distribution, Figure 5 (b) and Figure 5 (c) demonstrated as well as The average simulation results of the two trajectories after 50 parameter corrections are compared with the measured trajectories and the simulated trajectories before parameter correction. Although the fit between the simulation and measured results is extremely significant after parameter correction, there are obvious differences in the parameter correction results. Gen1- The perturbation result was 19.1838 s, and the correction result ranged from 18.0132 s to 20.8447 s, with deviations from the perturbation result of this parameter ranging from -6.10% to 8.66%; for parameter Gen1- The perturbation result is 0.2134, while the correction result of this parameter ranges from 0.1645 pu to 0.2556 pu, with a deviation of -22.92% to 19.75%.

[0207] From a numerical perspective, although the parameter Gen1- The deviation range is less than the parameter Gen1- Parameter Gen1- The multiple solutions seem to be more severe, but this does not mean that the parameters Gen1- The correction results are accurate, a phenomenon due to the parameter Gen1- It is determined by its numerical compensation. The linear relationship fitted by these 50 sets of solutions indicates that the parameter Gen1- and Gen1- They have a strong negative correlation, and the correlation coefficient is... Reaching -0.972, the relationship, after fitting, can form a linear function:

[0208] ;

[0209] This phenomenon indicates that Based on the collinearity parameters identified by sensitivity trajectory analysis, The parameter Gen1- cannot be implemented. and Gen1- The high degree of identification is due to the obvious numerical compensation phenomenon of the two parameters, making it impossible to effectively correct such parameters.

[0210] 3. Risk verification based on conditional collinearity parameter correction.

[0211] This example applies the high-risk scoring parameter to A(Gen1- & Gen1- , ) and low-risk scoring parameters for B (Gen1- & Gen2- , The calculations are compared. The solution method and related settings are consistent with Example 2. It should be noted that there is a possibility that the true value of the conditional collinearity parameter may fall exactly in the collinearity interval. The probability of this occurring is equivalent to the probability of this parameter pair in a large number of perturbation samples. overthreshold frequency This risk can be reduced by lowering its threshold. For the calibration of such parameters, we focus more on their origin... Insufficient information can lead to convergence oscillations or degradation problems during the iteration process. The degree of oscillation during iterative solution can be statistically analyzed based on the following indicators.

[0212] Define parameters to update path tortuosity, and denote the first... The contemporary optimal parameter vector is Then the parameter update path tortuosity Defined as:

[0213] ;

[0214] in This represents the total distance of the parameter update path. This is the net displacement from the starting point to the ending point. This equation measures the degree to which particles travel back and forth in the update path. If the search tends to stabilize and converge, the total distance traveled by the particles is close to the net displacement. When the parameter update manifests as repeated adjustments within a certain numerical range, the total distance traveled by the particle will be significantly greater than the net displacement.

[0215] Based on the results of 50 parameter corrections under the initial random particle distribution, based on Gen1- & Gen1- The average correction trajectory of the two-parameter correction values ​​in 50 simulation results is as follows: Figure 6 (a) Figure 6 As shown in (b), based on Gen1- &Gen2- The simulated trajectory of the two-parameter correction values ​​is as follows Figure 6 (c) Figure 6 As shown in (d), it is intuitively clear that the trajectory fits the measured results significantly better after parameter correction. Parameter Gen1- With Gen1- The perturbated true values ​​are 0.6375 s and 0.2078 pu, respectively. Among all the calibrated samples, the parameter Gen1- With Gen1- The maximum relative errors from the true values ​​are 5.83% and 0.386%, respectively, with a correlation coefficient of -0.013, indicating that the parameters are uncorrelated. For Gen1- & Gen2- The two parameters have true values ​​of 0.2740 pu and 0.1684 pu, respectively, and the maximum relative errors between the samples and the true values ​​are 0.54% and 2.27%. The above results demonstrate the reliability of the parameter solution.

[0216] Further comparison of the parameter update path tortuosity between parameter pair A and parameter pair B It is evident that the two methods exhibit significant differences in path efficiency and directional consistency during the iterative process. For parameter pair A, The median value reached 7.14, ranging from 1.06 to 18.55. This indicates that only a small number of samples exhibit strong directional consistency in parameter updates, with update paths approaching end-to-end displacements, i.e., high path efficiency. However, in most samples, the cumulative variation of the parameter update path is much greater than the final net displacement, manifested as a significant increase in tortuosity. This phenomenon implies that the "current best" parameter position undergoes repeated back-and-forth migrations within the parameter space during iteration, significantly lengthening the update path. This low path efficiency is particularly pronounced when the objective function has a relatively flat valley or when there are approximately equivalent alternative directions. In contrast, the parameter's relationship to B... The overall distribution is more concentrated and the level is lower, indicating that its parameter update path is closer to monotonic advancement, the direction of the iteration process is more consistent, and thus it exhibits more stable convergence behavior.

[0217] The computational results provided by this invention demonstrate that the sensitivity trajectory reconstruction characterization method proposed in this invention can effectively preserve the main dynamic morphology and key mechanistic information of the original trajectory. After training, the median correlation coefficient between the reconstructed trajectory and the original trajectory reached 0.9611, the mean reached 0.9206, and the median RMSE decreased from 0.1253 to 0.0306. Simultaneously, the sMAPE of the attenuation index of the active power trajectory and voltage trajectory at node 8 were 7.26% and 9.60%, respectively, indicating that this method can not only reconstruct the trajectory waveform but also effectively retain the attenuation characteristic information closely related to parameter identification, providing a reliable basis for subsequent comparison of parameter action directions.

[0218] Furthermore, after analyzing 630 parameter pairs formed from 36 target parameters, the example identified 1 stable collinear parameter pair, 619 stable non-collinear parameter pairs, and 10 conditionally collinear parameter pairs. Among them, the stable collinear parameter pair Gen1- and Gen1- The collinearity over-limit frequency reached 94.35%, and the fluctuation was only 2.61%, indicating that the present invention can effectively identify parameter pairs that are difficult to distinguish in the long term before the parameter verification is implemented, and realize quantitative diagnosis of the separability state of different parameters.

[0219] In the calibration verification, the parameter pairs identified as stable collinear Gen1- and Gen1- Although a good trajectory fit can be achieved, the results of 50 random initial value corrections show a significant compensation relationship, and the correlation coefficient between the two parameters reaches -0.972, indicating that there are obvious multiple solutions and substitution phenomena for the parameter pair, which verifies the ability of this invention to predict global unidentifiable risks.

[0220] For conditionally collinear parameter pairs, this invention also verifies its predictive ability for iterative degradation and convergence instability risks. A case study compares high-risk parameter pair A and low-risk parameter pair B. After parameter correction for both sets, the simulated trajectories closely match the measured trajectories, and the overall parameter solution results remain within a reasonable error range. However, in terms of parameter update path tortuosity, parameter pair A has a median of 7.14, ranging from 1.06 to 18.55, exhibiting significant back-and-forth wandering and low path efficiency. In contrast, parameter pair B has a more concentrated and lower tortuosity distribution, with an update path closer to monotonic progression and a more stable convergence process. These results demonstrate that the risk score constructed in this invention not only distinguishes between "identifiable" and "unidentifiable" parameters but also reflects the stability differences of different parameter pairs in subsequent verification iterations, providing a good explanation for identifying local oscillations, stagnation, and iterative degradation risks.

[0221] In summary, this invention, through a technical path of "trajectory reconstruction representation—collinearity classification—risk assessment," achieves prior analysis of the effectiveness of the feature system before parameter verification. Its effects are manifested in: identifying the persistent unidentifiable risk corresponding to stable collinearity before parameter verification, identifying the local degradation and instability risks corresponding to conditional collinearity, and providing a basis for target parameter selection, feature supplementation, and verification strategy adjustment. This helps reduce the probability of multiple solutions, compensation, and convergence degradation problems, and improves the stability and reliability of the parameter verification process.

[0222] This invention also provides a priori diagnostic device 800 for the identifiability of power system model parameters, comprising:

[0223] The construction module 801 is used to construct disturbance samples within the prior range of parameters and generate a multi-channel trajectory sensitivity sample library. Specifically, it includes: determining the set of candidate parameters to be diagnosed and their prior value range; performing multiple sets of disturbance sampling on each candidate parameter within the prior value range to obtain disturbance samples covering different parameter states; and for each set of disturbance samples, calculating the trajectory sensitivity of each candidate parameter to the target observation based on power system transient simulation to construct a multi-channel trajectory sensitivity sample library.

[0224] The learning module 802 is used to perform mechanism-guided reconstruction representation learning on the trajectories in the multi-channel trajectory sensitivity sample library, construct a mechanism-guided trajectory reconstruction representation mechanism, and map information related to the target features to a unified representation space.

[0225] The diagnostic module 803 is used to measure the differences and overlaps in the response directions of different parameters under a given feature system based on the obtained trajectory characterization results, determine the relationship between parameters, and form collinearity diagnostic results oriented towards parameter identification sufficiency.

[0226] The judgment module 804 is used to assess the risk of multiple solutions, compensation and iterative degradation under a given characteristic system based on the results of parameter separability and collinearity diagnosis, and to identify verifiable parameters.

[0227] According to embodiments of the present invention, an electronic device 900 is also provided, such as... Figure 9 As shown, it includes a memory 901, a processor 902, and a computer program stored in the memory 901 and executable on the processor. When the processor 902 executes the program, it implements the steps of the method described in any of the above embodiments.

[0228] According to embodiments of the present invention, a computer-readable storage medium is also provided, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the steps of the method described in any of the above embodiments.

[0229] This invention also provides a computer program product, including a computer program stored in a computer-readable storage medium; when a processor of an electronic device reads the computer program from the computer-readable storage medium, the processor executes the computer program, causing the electronic device to perform the steps of any of the methods described in the above embodiments.

[0230] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0231] It should be understood that the specific embodiments described above are merely illustrative or explanatory of the principles of the present invention and do not constitute a limitation thereof. Therefore, any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and scope of the present invention should be included within the protection scope of the present invention.

Claims

1. A priori diagnostic method for the identifiability of power system model parameters, characterized in that, include: The process involves constructing disturbance samples within the prior range of parameters and generating a multi-channel trajectory sensitivity sample library. Specifically, this includes: determining the set of candidate parameters to be diagnosed and their prior value ranges; performing multiple sets of disturbance sampling on each candidate parameter within the prior value range to obtain disturbance samples covering different parameter states; and for each set of disturbance samples, calculating the trajectory sensitivity of each candidate parameter to the target observation based on power system transient simulation to construct a multi-channel trajectory sensitivity sample library. The trajectory in the multi-channel trajectory sensitivity sample library is subjected to mechanism-guided reconstruction representation learning to construct a mechanism-guided trajectory reconstruction representation mechanism, which maps information related to target features to a unified representation space; Based on the obtained trajectory characterization results, the differences and overlap of response directions of different parameters under a given feature system are measured, the relationship between parameters is judged, and collinearity diagnosis results oriented towards parameter identification sufficiency are formed. Based on the results of parameter separability and collinearity diagnosis, assess the risks of multiple solutions, compensation and iterative degradation under a given characteristic system, and identify verifiable parameters; The mechanism-guided reconstruction representation learning includes: The encoding process is defined using Formula 3, as follows: （3）； In the formula, Indicates the first Parameters for each sample The low-dimensional latent space representation; Represents the encoding mapping function; The input multi-channel sensitivity trajectory is represented by an encoder using a one-dimensional convolutional network and a decoder using a multilayer perceptron to achieve low-dimensional encoding and trajectory reconstruction of the multi-channel sensitivity trajectory. The trajectory reconstruction loss function is expressed as shown in Formula 4, as follows: （4）； In the formula, Indicates the reconstruction loss; This represents the reconstructed trajectory output by the decoder; Represents the original input trajectory; Indicates smoothness Loss function; Define the continuous feature supervision loss function as shown in Formula 5, as follows: （5）； In the formula, This represents the monitoring loss for continuous mechanism characteristics; Indicates the total number of perturbed samples; Indicates the index of the perturbation sample; This indicates the total number of candidate parameters to be diagnosed; Indicates the index of the candidate parameter; The number of dimensions representing continuous mechanism features; Indicates continuous mechanism feature index, ; Indicates the first The nth perturbation sample The first candidate parameter corresponds to the sensitivity trajectory of the first... One true continuous mechanism characteristic value; This represents the corresponding continuous mechanism feature value predicted by the model; Indicates the first Weighting coefficients for continuous mechanism features; This represents the loss function for continuous feature regression, using mean squared error loss, mean absolute error loss, or smoothing loss. The loss, the continuous mechanism features include one or more of the following: trajectory decay exponent, dominant frequency, peak value, trough value, peak occurrence time, trough occurrence time, and recovery time; Let the oscillation prediction probability of the gated branch output be... Its corresponding tag is According to the explicit oscillation intensity index of the sample Constructing oscillation credibility Its definition is shown in Formula 6: （6）； in, The threshold for judging oscillation intensity is set at the middle position of the normalized intensity, i.e., the boundary between weak and strong oscillations. The confidence mapping coefficients and the definition of the oscillation confidence constraint gated loss are shown in Equation 7: （7）； In the formula, This represents the oscillation confidence constraint gated loss; This represents a category-related weighting function used to mitigate the imbalance between positive and negative samples. This represents the binary cross-entropy loss; This is a penalty term for boundary ambiguity, when the predicted probability is close to... When the value is relatively large, it is used to suppress ambiguous decisions on high-confidence samples; This represents the oscillation confidence level obtained from the explicit oscillation intensity mapping; This is a credibility consistency term used to constrain the gated output to maintain consistency with the actual oscillation strength of the sample. and These are the weight coefficients for the boundary ambiguity penalty term and the credibility consistency term, respectively. By combining trajectory reconstruction constraints, continuous feature supervision constraints, and oscillation confidence constraint gated loss, the total loss function is determined as shown in Formula 8, as follows: （8）； In the formula, Indicates the total loss; This represents a continuous feature supervision weight function that gradually increases during the training process; Indicates the current number of training steps or training round; This indicates the maximum number of preheating steps or preheating cycles; This represents the maximum weight for continuous feature supervision; This represents a gated switch; when the oscillation-related semantics belong to the features of interest in the current task, it is selected. Otherwise take ; The measurement of the differences and overlaps in the response directions of different parameters under a given characteristic system specifically includes: The latent space vectors corresponding to all samples and all parameters are treated as the population sample set, and the population covariance matrix is ​​calculated. The Mahalanobis metric matrix As the inverse of the overall covariance matrix ; Specifically, in the Under a perturbation sample, the parameter With parameters The consistency of the direction of action is given by the cosine similarity under the Mahalanobis metric, expressed by Formula Nine: （9）； In the formula, Indicates the first Parameters under a perturbation sample With parameters Similarity; Indicates the index of the perturbation sample; and Indicates the index of the candidate parameter, and ; and They represent the first Parameters under a perturbation sample and parameters The low-dimensional latent space vector; This represents the population mean vector calculated from the latent space vectors of all perturbation samples and all candidate parameters; The Mahalanobis metric matrix is ​​obtained from the inverse of the population covariance matrix. This represents the transpose of a vector. The closer the value is to 1, the more consistent the direction of influence of the two parameters on the dynamic response of the system under the current characteristic system, and the stronger their substitutability.

2. The method according to claim 1, characterized in that, The trajectory sensitivity is obtained using the central difference method, as follows: For any parameter 'a' to be analyzed, its trajectory sensitivity is obtained using the central difference method, as shown in Formula 1: （1）； In the formula, Indicates time, Indicates parameters Sensitivity to system trajectory; Indicates parameters The amount of minute perturbation; and They represent the parameter values ​​respectively. and The corresponding state trajectory at that time; and These represent the corresponding algebraic variable trajectories.

3. The method according to claim 1, characterized in that, The construction of the multi-channel trajectory sensitivity sample library specifically includes: Obtained through Latin hypercube sampling Group of perturbation samples, the system has a total of The candidate parameters, and the multi-channel trajectory sensitivity sample library, are expressed by Formula 2, as follows: （2）； In the formula, This represents a multi-channel trajectory sensitivity sample library; Indicates the total number of perturbed samples; This indicates the total number of candidate parameters to be diagnosed; This indicates the index of the perturbation sample. ; Indicates the index of the candidate parameter. ; Indicates the first The nth perturbation sample The multi-channel sensitivity trajectory corresponding to each candidate parameter, and ,in Indicates the number of observation channels. The sequence length after time alignment is indicated; the multi-channel trajectory sensitivity sample library is used to cover the parameter state regions experienced during the parameter calibration process.

4. The method according to claim 1, characterized in that, The relationship between the judgment parameters specifically includes: The frequency and degree of collinearity within the statistical sample domain are used to classify collinearity patterns, including: For parameter pairs In all The similarity results are calculated on each perturbed sample. Therefore, a sample-level similarity exceeding a threshold is defined. The frequency is shown in Formula 10: （10）； In the formula, Indicates parameter pair The frequency that exceeds the limit; and Indicates the index of the candidate parameter, and ; Indicates the total number of perturbed samples; Indicates the index of the perturbation sample; Indicates the first Parameters under a perturbation sample With parameters Similarity; This indicates the threshold for determining if the similarity exceeds the limit; This indicates an indicator function that takes the value 1 when the condition in parentheses is true and 0 otherwise. It is used to characterize the frequency of high consistency events occurring in all perturbed samples. To characterize the degree of discrimination when similarity falls below a threshold, a drop threshold is defined, as shown in Formula 11: （11）； In the formula, Indicates parameter pair In the Relative threshold for each sample The amount of the drop; when hour, ;when hour, The larger the value, the easier it is for the two parameters to be distinguished in this sample; Therefore, the volatility index is defined using Formula Twelve: （12）； In the formula, Indicates parameter pair The degree of fluctuation; Indicates parameter pair The frequency that exceeds the limit; and Indicates the index of the perturbation sample; and Representing parameter pairs respectively In the The and the first Similarity drop under each perturbation sample; Indicates parameter pair The average drop across all perturbation samples; Represents a very small positive number used to avoid a denominator of zero; prefix. Formula 12 is used to reduce the artificially high impact of a very small number of samples that do not exceed the limit or a very small number of samples that fall below the threshold on volatility. It reflects the degree to which the parameters depend on the separability of the parameters on the changes in the parameter state. Based on over-limit frequency and volatility The collinearity modes of parameters are divided into three categories; Set threshold and volatility threshold ,in It is used simultaneously for determining sample-level similarity exceeding limits and determining the frequency of exceeding limits; among which... , ;when and When the parameter pair is determined to be a stable collinear parameter pair, it is considered to be a stable collinear parameter pair. when When the parameter pair is determined to be a stable noncollinear parameter pair; In other cases, the parameter pair is determined to be a conditionally collinear parameter pair.

5. The method according to claim 1, characterized in that, The assessment evaluates the risks of multiple solutions, compensation, and iterative degradation under a given characteristic system, and identifies verifiable parameters, specifically including: To characterize whether a parameter pair exhibits a stable and significant indistinguishable relationship over the long term across all perturbed samples, a parameter pair is defined. The risk of global collinearity is shown in Formula Thirteen: （13）； In the formula, Indicates parameter pair The risk of global collinearity; Indicates parameter pair The frequency that exceeds the limit; Indicates parameter pair The degree of fluctuation; To characterize whether collinear-noncollinear state switching occurs between parameter pairs in the local parameter space, define parameter pairs. In the The collinear event labels for each perturbation sample are defined using Formula Fourteen: （14）； In the formula, Indicates parameter pair In the Does a collinear event occur under each perturbation sample? This indicates an indicator function that takes the value 1 if the condition within the parentheses is true, and 0 otherwise. Indicates the first Parameters under a perturbation sample With parameters Similarity; This indicates the threshold for determining if the similarity exceeds the limit; when When, it indicates that the parameter is relative to the sample. Collinearity event occurs; when When, it indicates that the parameter is relative to the sample. No collinearity events occurred; Let the first The parameter vector of each perturbation sample is Constructed based on Euclidean distance between samples Nearest neighbor graph, whose edge set is denoted as If the collinear event labels of samples at both ends of an edge are different, it is considered that the identifiability of that parameter pair has switched under local small-range parameter changes. The local flip rate is defined as shown in Formula 15: （15）； In the formula, Indicates parameter pair Local flip rate; This indicates that the vector is constructed based on the perturbation sample parameter vector. Edge set of a nearest neighbor graph; Representing edge set The number of edges contained therein; Let an edge in the nearest neighbor graph be an edge that connects the first and second neighbors. The first perturbation sample and the second One perturbation sample; and Representing parameter pairs respectively In the The and the first Collinear event labels under a perturbation sample; This represents the XOR operation, where 1 is returned when the two labels are different, and 0 is returned when they are the same. The larger the value, the better the parameter. The more easily the transition between collinear and non-collinear states occurs in the local parameter space; Define a two-state coexistence gating factor, as shown in Formula 16: （16）； In the formula, Indicates parameter pair Two-state coexisting gating factor; Indicates parameter pair The frequency of exceeding the limit; coefficient 4 is the normalization coefficient, making The range of values ​​is ;when A value close to 0 indicates that the parameters are not collinear. When the value is close to 1, it indicates that the parameters are collinear. Approaching 0; when When the condition is such that collinear and non-collinear states coexist to the highest degree, then... The maximum value is 1. Define parameter pairs The risk of partial handover is addressed using Formula 17: （17）； In the formula, Indicates parameter pair Risk of partial switching; This represents a gating factor indicating the coexistence of two states; The formula represents the local flip rate. Formula 17 considers whether the parameter pair exists in both collinear and non-collinear states in the sample domain, and whether it is easy for the state to switch in the local parameter space. It is mainly used to characterize the risk of oscillation, stagnation or path degradation caused by conditional collinear parameter pairs in subsequent iterative verification. The total risk score is defined using Formula 18: （18）； In the formula, Indicates parameter pair Overall risk score; Indicates parameter pair The risk of global collinearity; Indicates parameter pair Risk of partial switching; This indicates taking the larger of the two values; when the parameter pair exhibits long-term stable collinearity, the total risk score is mainly dominated by global collinearity risk; when the parameter pair exhibits conditional collinearity, the total risk score is mainly dominated by local switching risk; when the parameter pair exhibits stable non-collinearity, the global collinearity risk and local switching risk are low, and the total risk score is low. Based on the total risk score, a parameter-based screening result is generated, specifically including: Let the set of parameters to be checked simultaneously be... Let the total risk threshold be... , For any candidate parameter If it is related to the set any other candidate parameter None of them constitute stable collinear parameter pairs, and the corresponding total risk scores Then determine the parameters Under a given feature system, it is suitable for direct verification; if the parameters With at least one candidate parameter They form stable collinear parameter pairs, or there exist For high-risk parameter pairs, then determine the parameter. It is not advisable to match the corresponding candidate parameters under the current feature system. Simultaneous verification requires fixing one of the parameters, merging parameter combinations, adding observation channels, supplementing mechanistic features, or adjusting the objective function before verification.

6. A priori diagnostic device for the identifiability of power system model parameters, characterized in that, include: The construction module is used to construct disturbance samples within the prior range of parameters and generate a multi-channel trajectory sensitivity sample library. Specifically, it includes: determining the set of candidate parameters to be diagnosed and their prior value range; performing multiple sets of disturbance sampling on each candidate parameter within the prior value range to obtain disturbance samples covering different parameter states; and for each set of disturbance samples, calculating the trajectory sensitivity of each candidate parameter to the target observation based on power system transient simulation to construct a multi-channel trajectory sensitivity sample library. The learning module is used to perform mechanism-guided reconstruction representation learning on the trajectories in the multi-channel trajectory sensitivity sample library, construct a mechanism-guided trajectory reconstruction representation mechanism, and map information related to target features to a unified representation space. The diagnostic module is used to measure the differences and overlaps in the response directions of different parameters under a given feature system based on the obtained trajectory representation results, determine the relationship between parameters, and form collinearity diagnostic results oriented towards the sufficiency of parameter identification. The judgment module is used to assess the risk of multiple solutions, compensation and iterative degradation under a given characteristic system based on the results of parameter separability and collinearity diagnosis, and to identify verifiable parameters. The mechanism-guided reconstruction representation learning includes: The encoding process is defined using Formula 3, as follows: （3）； In the formula, Indicates the first Parameters for each sample The low-dimensional latent space representation; Represents the encoding mapping function; The input multi-channel sensitivity trajectory is represented by an encoder using a one-dimensional convolutional network and a decoder using a multilayer perceptron to achieve low-dimensional encoding and trajectory reconstruction of the multi-channel sensitivity trajectory. The trajectory reconstruction loss function is expressed as shown in Formula 4, as follows: （4）； In the formula, Indicates the reconstruction loss; This represents the reconstructed trajectory output by the decoder; Represents the original input trajectory; Indicates smoothness Loss function; Define the continuous feature supervision loss function as shown in Formula 5, as follows: （5）； In the formula, This represents the monitoring loss for continuous mechanism characteristics; Indicates the total number of perturbed samples; Indicates the index of the perturbation sample; This indicates the total number of candidate parameters to be diagnosed; Indicates the index of the candidate parameter; The number of dimensions representing continuous mechanism features; Indicates continuous mechanism feature index, ; Indicates the first The nth perturbation sample The first candidate parameter corresponds to the sensitivity trajectory of the first... One true continuous mechanism characteristic value; This represents the corresponding continuous mechanism feature value predicted by the model; Indicates the first Weighting coefficients for continuous mechanism features; This represents the loss function for continuous feature regression, using mean squared error loss, mean absolute error loss, or smoothing loss. The loss, the continuous mechanism features include one or more of the following: trajectory decay exponent, dominant frequency, peak value, trough value, peak occurrence time, trough occurrence time, and recovery time; Let the oscillation prediction probability of the gated branch output be... Its corresponding tag is According to the explicit oscillation intensity index of the sample Constructing oscillation credibility Its definition is shown in Formula 6: （6）； in, The threshold for judging oscillation intensity is set at the middle position of the normalized intensity, i.e., the boundary between weak and strong oscillations. The confidence mapping coefficients and the definition of the oscillation confidence constraint gated loss are shown in Equation 7: （7）； In the formula, This represents the oscillation confidence constraint gated loss; This represents a category-related weighting function used to mitigate the imbalance between positive and negative samples. This represents the binary cross-entropy loss; This is a penalty term for boundary ambiguity, when the predicted probability is close to... When the value is relatively large, it is used to suppress ambiguous decisions on high-confidence samples; This represents the oscillation confidence level obtained from the explicit oscillation intensity mapping; This is a credibility consistency term used to constrain the gated output to maintain consistency with the actual oscillation strength of the sample. and These are the weight coefficients for the boundary ambiguity penalty term and the credibility consistency term, respectively. By combining trajectory reconstruction constraints, continuous feature supervision constraints, and oscillation confidence constraint gated loss, the total loss function is determined as shown in Formula 8, as follows: （8）； In the formula, Indicates the total loss; This represents a continuous feature supervision weight function that gradually increases during the training process; Indicates the current number of training steps or training round; This indicates the maximum number of preheating steps or preheating cycles; This represents the maximum weight for continuous feature supervision; This represents a gated switch; when the oscillation-related semantics belong to the features of interest in the current task, it is selected. Otherwise take ; The measurement of the differences and overlaps in the response directions of different parameters under a given characteristic system specifically includes: The latent space vectors corresponding to all samples and all parameters are treated as the population sample set, and the population covariance matrix is ​​calculated. The Mahalanobis metric matrix As the inverse of the overall covariance matrix ; Specifically, in the Under a perturbation sample, the parameter With parameters The consistency of the direction of action is given by the cosine similarity under the Mahalanobis metric, expressed by Formula Nine: （9）； In the formula, Indicates the first Parameters under a perturbation sample With parameters Similarity; Indicates the index of the perturbation sample; and Indicates the index of the candidate parameter, and ; and They represent the first Parameters under a perturbation sample and parameters The low-dimensional latent space vector; This represents the population mean vector calculated from the latent space vectors of all perturbation samples and all candidate parameters; The Mahalanobis metric matrix is ​​obtained from the inverse of the population covariance matrix. This represents the transpose of a vector. The closer the value is to 1, the more consistent the direction of influence of the two parameters on the dynamic response of the system under the current characteristic system, and the stronger their substitutability.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method according to any one of claims 1-5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-5.

Images